Pieri resolutions for classical groups

TL;DR

This paper extends the construction of equivariant minimal free resolutions from the general linear group to orthogonal and symplectic groups, and explores equivariant Boij-S"oderberg decompositions.

Contribution

It introduces new equivariant resolutions for classical groups and proposes conjectures on equivariant Betti table decompositions, expanding the algebraic understanding of these structures.

Findings

Constructed equivariant resolutions over orthogonal and symplectic groups.

Provided partial results and examples for equivariant Boij-S"oderberg decompositions.

Generalized existing resolutions from the general linear group to classical groups.

Abstract

We generalize the constructions of Eisenbud, Fl{\o}ystad, and Weyman for equivariant minimal free resolutions over the general linear group, and we construct equivariant resolutions over the orthogonal and symplectic groups. We also conjecture and provide some partial results for the existence of an equivariant analogue of Boij-S\"oderberg decompositions for Betti tables, which were proven to exist in the non-equivariant setting by Eisenbud and Schreyer. Many examples are given.